Average Error: 18.8 → 1.3
Time: 11.9s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}
double f(double u, double v, double t1) {
        double r417199 = t1;
        double r417200 = -r417199;
        double r417201 = v;
        double r417202 = r417200 * r417201;
        double r417203 = u;
        double r417204 = r417199 + r417203;
        double r417205 = r417204 * r417204;
        double r417206 = r417202 / r417205;
        return r417206;
}
↓
double f(double u, double v, double t1) {
        double r417207 = v;
        double r417208 = u;
        double r417209 = t1;
        double r417210 = r417208 + r417209;
        double r417211 = r417207 / r417210;
        double r417212 = -r417209;
        double r417213 = r417211 * r417212;
        double r417214 = r417213 / r417210;
        return r417214;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.8

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.2

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  4. Using strategy rm

  5. Applied associate-*l/1.3

    \[\leadsto \color{blue}{\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}}\]

  6. Final simplification1.3

    \[\leadsto \frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}\]

Reproduce

herbie shell --seed 2019128 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))